In Conceptual Algebra we emphasize clear, precise, and mathematically accurate communication skills. Some time is spent discussing correct mathematical grammar, for example. The Cover Sheet assignment used in Conceptual Algebra, which is a modification of the general-purpose Cover Sheet assignment provided at the link, allows teachers to practice and improve their ability to communicate precisely and correctly when writing in mathematics. One middle school teacher, following a discussion of the difference between a function and an equation, for example, raised her hand and then announced with some humor, "Dr. Barzilai, we are the root of your problems referring to the insufficient preparation of first-year college students in correct mathematical grammar as having roots in the middle school years.

The modified Cover Sheet assignments also foster introspection. For while it is certainly true that careful thinking ahead of writing helps the quality of one's writing, including in mathematics, it is also true that the very process of having to write down one's thoughts in detail and with precision, helps sharpen one's mathematical understanding. And since the Cover Sheets include an optional but usually implemented "questions" section, they also allow teachers in Conceptual Algebra to share their questions and/or confusions with their instructor for personalized feedback. The Cover-sheet assignments are, like many worthwhile exercises that stretch one's abilities, mentally challenging and some weeks, time-consuming. Unlike the general purpose Cover Sheet, we do not require a Cover Sheet every week of the course, however.

Another important facet of this assignment has been articulated by many teachers who have taken Conceptual Algebra: that teachers, once they have experienced written assignments with them as student, have gained experience, confidence, and greater readiness to try out (or delve more deeply into) the use of written assignments in their own courses in a way that helps their students deepen their mathematical understandings, and in a way which is flexible enough so that modifications can be used which fit the time constraints on their students and on them as graders, evaluators, and/or feedback providers.

The Three-Part Concept Map (or "Concept Web") assignment is a favorite for teachers. The directions are self explanatory, but the making of the concept map for one's own algebra course (be it pre-algebra, Algebra I, etc), and the expansion thereof into three parts including "inputs" or prerequisite skills, and "outputs" or applications and uses in future courses, are further enhanced when teachers compare their Three-Part Concept Maps with one another in heterogeneous groups; then re-visit their Maps to change, or improve, or further flesh them out based on this input from fellow teachers as well as based on suggestions and questions from the instructor and T.A.

Introspection is also encouraged and even formalized in the individual and/or groupwork assignment on technology. Virtually everyone uses the phrase "appropriate technology" these days, yet how often have you heard the term defined or even explained? In this activity, teachers are supported as they work to define criteria that best fit their own teaching, for what "appropriate" means to them. While the process is not a simple rubric, this exercise shares some similarities with exercises aiding teacher to develop rubrics for what key components of an assignment should look like. In this sense, the assignment is a meta-worksheet in that teachers who have gone though the exercise can more easily create their own sets of criteria for use in a wider variety of situations regarding technology or even other aspects of teaching.